Parameter estimation for and use of a thermal model of a power line

ABSTRACT

A relationship between a temperature T&lt;SUB&gt;l &lt;/SUB&gt;of a power line or power transmission conductor 10, an electrical quantity of the power line such as a current l or power flow P through the power line, as well as meteorological quantities or ambient conditions of the power line such as wind speed W, wind direction, humidity, solar radiation S and ambient temperature T&lt;SUB&gt;a&lt;/SUB&gt;, is established in the form of a thermal model of the power line. Values of the aforementioned quantities or variables are continuously measured, and the collected values of the quantities are evaluated in order to update model parameters of the thermal model during operation of the power line. In an exemplary embodiment, an average temperature representative of the entire line is determined via two phasor measurement units (PMU) 11, 11&#39; providing synchronized phasor values from two ends of the power line. An ohmic resistance of the power line can be computed from the phasor values, from which in turn the average line temperature can be derived.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation-in-part application under 35 U.S.C.§120 which claims the benefit of the filing date of allowed U.S. patentapplication Ser. No. 10/499,701, fled May 3, 2005 as a 35 U.S.C. §371application of PCT/CH02/00682 filed Dec. 11, 2002, and which in returnclaims priority under 35 U.S.C. §119 to European Patent Application No.1811254.0, filed on Dec. 21, 2001 in the European Patent Office, thedisclosures of which are all incorporated herein in their entireties byreference.

BACKGROUND

An operation of electric power transmission lines is disclosed.

As a consequence of the electric utility industry deregulation andliberalization of electricity markets, the amount of electric powerexchanged between remote regions and trading activities betweendifferent countries are steadily increasing. In addition, due to theemerging desire to optimize assets, substantially increased amounts ofpower are transmitted through the existing networks, occasionallycausing congestion, transmission bottlenecks and/or oscillations ofparts of the power transmission systems. In particular, thermalconstraints can impose limitations on power flow in critical power flowpaths or power transmission corridors interconnecting distinct areas.Exemplary reasons for these thermal constraints are an annealing ofand/or a permanent damage to the conductors caused by severe overloadsas well as an increase in conductor length with the temperature of thepower line conductor. The latter may lead to unsatisfactory groundclearance due to line sag and possible flash-over to nearby trees orother line conductors, with subsequent trip by the protection system asa result.

A number of symptoms or effects relate to an elevated line temperatureand therefore can influence the maximum allowable temperature of aspecific electric power transmission line. Among the former are adegradation of mechanical properties of the conductors and connectors(loss of mechanical strength and integrity as well as acceleratedcomponent aging), an increase in conductor sag, an increase in resistivelosses, and a potential damage to devices or equipment attached to theconductors (e.g. for power line communication).

Both the maximum allowable conductor temperature and the worst-caseweather conditions used in calculating line ratings are selected by theindividual network owners or independent Transmission System Operators(TSO). The operational temperature for a specific overhead power linesgenerally varies between, for example, 50 and 100° C.

Since the line temperature is not measurable in a straight forward way,an alternative limit in terms of maximum allowable power transfer ormaximum allowable current can be derived based on worst-case scenarioassumptions. This limit is usually referred to as the “ampacity” of theline. The additional assumptions made can be subjective, and/or theresulting thermal limits in terms of power transfer or current can bemade on a somewhat ad-hoc basis. Also, since they are based on aworst-case scenario, they can be unnecessarily conservative.Consequentially, direct monitoring of the thermal limits in terms oftemperature instead of power transfer or current can be provided usingan on-line measurement of the line temperature in order to evaluate,during operation, whether a line is loaded close to its operationaltemperature limit or not.

A number of techniques have been proposed and several products areavailable to measure or infer the temperature of power line conductorsduring operation. These comprise the use of infrared cameras, mechanicaltension measurements, direct sag measurements, predictive meteorologicalmethods, or the use of phasor measurement data.

Infrared cameras may be used to take a digital picture of a power line,the color information of which is subsequently analyzed in a signalprocessing step in order to derive the temperature of the conductors.This technique can perform monitoring of the temperature of particularhotspots that are known a-priori.

Mechanical tension measurements between the tower and the isolator incombination with solar radiation and ambient temperature measurementscan be based on the fact that the tension of the line conductor isapproximately inversely proportional to its length. From therelationship between tension and length of the conductor, the line sagof a single span and the conductor temperature can be inferred.Likewise, line sag monitors directly measure the line sag of a singlespan through for example GPS (global positioning system) or lasermeasurement techniques.

Predictive meteorological methods and products based on the IEEE738-1993 “Standard for Calculating the Current-Temperature of BareOverhead Conductors”, the disclosure of which is incorporated herein byreference in its entirety, have been proposed to model the dependencybetween the line ampacity and various operational and ambientproperties. These methods involve a number of meteorologicalmeasurements such as air temperature, wind speed, angle between wind andconductor and the elevation above sea level. The IEEE 738-1993 standardthen specifies a computational procedure that can be used to estimate asteady-state conductor temperature from the meteorological measurementsalone, i.e. without reverting to an independent measurement of the linetemperature. The standard is based on a purely static model which doesnot account for the time-dependent behaviour of the line temperature andwhich is difficult to tune since various input parameter data may beassumed and detailed meteorological data is required.

The patent application EP 1324454, the contents of which are herebyincorporated herein by reference, describes a way of determining anactual average conductor temperature, via a calculated seriesresistance, from on-line phasor measurements. The average linetemperature is largely independent of assumptions regarding any lineparameters, such as the inductance, reactance or susceptance of thepower line conductor. The method includes determining time-stampedcurrent phasor information and voltage phasor information for a firstend and a second end of the line, computing an ohmic resistance of theline from the phasor information, and computing an average linetemperature from the ohmic resistance.

A state or condition of an electric power system at one specific pointin time can be obtained from a plurality of synchronized phasormeasurements or snapshots collected across the electric power system orpower transmission network. Phasors are time-stamped, complex valuessuch as amplitude and phase, of local electric quantities such ascurrents, voltages and load flows, and can be provided by means ofPhasor Measurement Units (PMU). These units involve a very accurateglobal time reference, obtained e.g. by using the Global PositioningSatellite (GPS) system or any other comparable means, and allowingsynchronization of the time-stamped values from different locations. Thephasors are sampled at, for example, a rate of 20 to 60 Hz with atemporal resolution of less than 1 millisecond, and thus can provide arather dynamic view on transient states that goes beyond the ratherstatic view as provided by scalar values such as RMS values of voltagesor currents and relied upon by SCADA/EMS systems.

Accordingly, parameters of an electric power network may be estimated byrepeatedly measuring, at a plurality of network locations, synchronizedvalues of electrical network variables; and identifying there from,during network operation, currently valid parameters of a mathematicalmodel of the power network. In particular and by way of example, thePatent Application EP-A 1 489 714, the contents of which areincorporated herein by reference, discloses an adaptive detection ofelectromechanical oscillations in electric power systems based on alinear time-varying model. A system quantity or signal such as e.g. theamplitude or angle of the voltage or current at a selected node of thenetwork is sampled, and the parameters of the linear model representingthe behaviour of the power system are estimated by means of Kalmanfiltering techniques. This process can be carried out in a recursivemanner, i.e. every time a new value of the system quantity is measuredthe parameters of the model are updated. Finally, from the estimatedparameters of the model, the parameters of the oscillatory modes, suchas frequency and damping, are deduced and presented to an operator. Thisadaptive identification process can provide a real-time analysis of thepresent state of the power system.

SUMMARY

A method and system are disclosed that can, at any time duringoperation, provide a reliable forecast of a power line conductortemperature. An exemplary method of estimating model parameters of athermal model of a power line as well as a use of the thermal model aredisclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter of the invention will be explained in more detail inthe following text with reference to preferred exemplary embodimentswhich are illustrated in the attached drawings, of which:

FIG. 1 schematically shows a power line with a number of measurementdevices,

FIG. 2 depicts a process of model parameter estimation, and

FIG. 3 depicts measured values of a number of quantities recorded for aperiod of 6 h.

The reference symbols used in the drawings, and their meanings, arelisted in summary form in the list of reference symbols. In principle,identical parts are provided with the same reference symbols in thefigures.

DETAILED DESCRIPTION

In accordance with exemplary embodiments, a relationship between atemperature of a power line or power transmission conductor, anelectrical quantity of the power line such as a current or power flowthrough the power line, as well as meteorological quantities or ambientconditions of the power line such as wind speed, wind direction,humidity, solar radiation and ambient temperature, can be established inthe form of a thermal model of the power line and repeatedly calculatedor updated during operation of the power line. To this end, values ofthe aforementioned quantities or variables can be continuously orperiodically measured or sampled, and the collected values of thequantities evaluated in order to update or tune model parameters of thethermal model. Including the temperature of the power line as a variableof the thermal model allows using, without diminishing its validity, asimple model or even a black box model with a limited number of modelparameters. The latter may be updated without excessive computationalefforts as frequently as desired, which ultimately increases thereliability, at any time during operation, of a forthcoming linetemperature prediction.

In an exemplary embodiment disclosed herein, an average temperaturerepresentative of the entire line is determined via two PhasorMeasurement Units (PMU) providing synchronized phasor values from twoends of the power line. An ohmic resistance of the power line iscomputed from the phasor values, from which in turn the average linetemperature can be derived. As the PMUs are primarily provided for otherpurposes, e.g. for determining electrical quantities, such a double useavoids the need for any dedicated line temperature sensing device. Inaddition, as the PMUs are generally mounted indoors in a protectedenvironment, they are less exposed to environmental stress than anyother line temperature sensing device.

On the other hand, it can be advantageous to calibrate the conversionfrom the resistance to the temperature of the power line by means ofsuch a dedicated line temperature sensor. As the latter may only betemporarily needed for the specific purpose of calibration, it may beexpensive or otherwise cumbersome without impairing the subsequentoperation of the power line.

In an exemplary variant, the meteorological data is obtained bysubscription and imported from an external source such as ameteorological institute which is distinct from the Transmission SystemOperator (TSO). Relying on the data from a specialist can, if desired,avoid dedicated measurement units located on or close to the lineconductor and operated by the TSO. Due to a relatively slow change inambient conditions and their small geographical gradients, any potentialtemporal or geographical offset between the meteorological data andelectrical data is of a lesser concern and can be ignored.

In an advantageous variant, an adaptive method or algorithm is based ona recursive calculation of the model parameters for each time-step,based on new values of the measured quantities and the old values of themodel parameters. As opposed to the collection of data over a timewindow and then performing the parameter identification at once, anychange in the power system can thus be detected much faster. In thiscontext, the thermal model can be a linear autoregressive model offinite order, and an adaptive Kalman Filter can be used to estimate itsmodel parameters.

The thermal model may be a nonlinear parametric model based on a heatbalance equation. Such a physically inspired model can offer higherconfidence when used for simulation, prediction or extrapolation and canbe used in place of, e.g. a linear parametric model with no physicalmeaning, such as an Auto-Regressive Moving Average model (ARMA). TheARMA model on the other hand has the advantage that, except for themodel order, no a-priori assumptions on model structure and parametershave to be made.

In a further aspect of an exemplary embodiment, the thermal model can beused to calculate a power line temperature given actual or forecastedvalues of electrical and meteorological quantities as e.g. provided byload predictions or weather forecasts. By comparing this predictedtemperature with a temperature limit for the power line, a maximumamount of current or electrical power flow that can be transported onthe line without violating the line temperature or sag limits may bederived, for example, by means of a simulation or inversion of thethermal model. Determination of a maximum flow that will result in acertain conductor temperature is particularly useful in order todetermine the actual power flow limits to be used in a balance marketclearing process. Since these limits are less conservative than a-prioriknown limits, less expensive balance power can be scheduled resulting inan economical gain for the TSO.

A computer program product is disclosed which includes computer programcode means for controlling one or more processors of a model parameterestimator, a line temperature predictor or a Power Flow Control deviceconnected to the power line. Such a computer program product can includea computer readable medium containing therein the computer program codemeans.

FIG. 1 shows a power line 10 that is part of a power system comprising aplurality of power generating means and power consumers interconnectedby a transmission network. At two ends of the power line, twosynchronized Phasor Measurement Units (PMU) 11, 11′ are provided and canbe mounted in respective substation control buildings or any desired,suitable location. Sensing devices for measuring meteorologicalquantities at one or more locations in the vicinity of the power line 10are collectively referred to as weather station 12. Means 13 formeasuring electrical quantities of the power line are depictedschematically, some of their components such as instrument transformersor process busses may also be used by the PMUs. An independent linetemperature measurement device 14 is likewise shown. The weather station12, the means 13 and the device 14 collect and provide a number ofequidistantly sampled measurements of ambient conditions (wind speed W,wind direction, solar radiation S, ambient temperature T_(a), humidity),electrical quantities (line current l, power flow P) and linetemperature (T_(l)) to a processor 15 of a model parameter estimator, aline temperature predictor or a Power Flow Control device.

FIG. 2 depicts an exemplary process of model parameter estimationaccording to an exemplary embodiment. The measured values of themeteorological and electrical quantities, collectively denoted as inputvariables u, are fed to the processor 15 for estimating or tuning, basedon parameter identification or fitting techniques such as Kalmanfilters, Maximum Likelihood or Least-Squares, values of model parametersA, B, . . . ; C_(l), . . . of a thermal model of the power line. Basedon the momentary values of the electrical and meteorological quantitiesas well as of the model parameters, a line temperature prediction T_(l)^(f) is produced as an output variable, and any difference between thelatter and a corresponding independent measurement of the linetemperature T_(l), is fed back for further evaluation.

The thermal model can be a standard linear black box model in transferfunction or state-space form. For dealing with several input variables uthe discrete-time state-space form:x(kT+T)=Ax(kT)+Bu(kT)+Ke(kT)  (a)y(kT)=Cx(kT)+Du(kT)+e(kT)  (b)x(0)=x0  (c)is the most convenient one. Here, x denotes the dynamic state of themodel, u the driving input variables, y the output of the system thatmodel should reproduce and e Gaussian white noise, whereas A, B, . . .are model parameters. Linear models are attractive because of the simpleparameter estimation techniques that are available and because of thefact that virtually no a-priori knowledge needs to be given, except forwhich measurements to use. On the other hand, such linear models canonly be used to predict the line behaviour with rather small variationsin the input variables, since non-linear contributions between theconductor temperature and the measured quantities could be quitesubstantial when the variations in the conductor temperature and/ormeasurement quantities are large. Accordingly, a linear model issuitable for short-term predictions on the order of minutes.Particularly a prediction interval of some 5-30 minutes (or lesser orgreater) can be used to compute dynamic ratings of power lines based ona 5-30 minute forecast (or lesser or greater) and based on theidentified dependencies between the conductor temperature and theelectrical and meteorological measurements. This rating can be mostbeneficially used in the market clearing for the balance market whichusually takes place on a similar time scale.

Alternatively, a physically inspired thermal model based on aheat-balance equation can have the advantage that model parameters whichare known with enough certainty can be fixed a-priori, wherein such athermal model could be valid also with quite large variations in theoperating points. However, such a model would be non-linear and caninvolve more complicated parameter estimation techniques than the linearblack box models. The extended Kalman filter has been shown to performwell in the estimation of parameters in non-linear models, although alsoother options are available. An exemplary heat balance equation has theform${{C_{l}\frac{\mathbb{d}T_{l}^{i}}{\mathbb{d}t}} = {{q_{i\quad n}( {I_{i}^{i},T_{a}^{i},{Solar}^{i},\ldots}\quad )} - {q_{out}( {T_{a}^{i},{Wind}^{i},\ldots}\quad )}}},$where C_(l) is a model parameter reflecting a characteristic thermaltime or thermal capacity of the line, and where q_(in) represents theincoming heat flow to the conductor with main contributions from thesun's radiation and the heat produced by resistive losses in theconductor, and where q_(out) is the total heat loss of the conductor.The heat loss depends on many factors, for example the radiation andconduction to the surrounding air which in turn depends on factors likethe wind speed and direction and the air humidity. The two heat transferterms can involve a number of further model parameters.

For prediction in the longer term a higher model order and long datasets can be used so that the daily and even weekly or monthly variationscan be modelled. Predictions based on such models could be used forexample in the computation dynamic ratings of lines in the day aheadmarket, which typically are executed 24 hours ahead with updateintervals of one hour.

FIG. 3 shows some measurement data from a field test, in which theweather and electrical phasor measurements were recorded during anobservation window of six hours following the connection of a 380 kVtransmission line at midday. The measured quantities are (top left plot)the conductor temperature (continuous line) and the ambient temperature(dashed line), the line current (top right plot) the humidity (middleleft plot), the wind speed (middle right plot) and the solar radiation(bottom plot) at a specific location along the line. The recordedmeasurement samples were evaluated for the identification of theparameters A, B, . . . of a first order discrete time state-space modelas indicated above, with the aim of accurately reproducing the linetemperature. On the basis of the identified model parameters, the effectof a 100 A increase in line current and of a one degree change inambient temperature have been simulated, yielding an increase in theline temperature of about 2.5° C. and 1° C. respectively.

The phasor data v₁, i₁; v₂, i₂ can be collected from phasor measurementunits that are distributed over a large geographical area, i.e. overtens to hundreds of kilometres. Since the phasor data from thesedisparate sources are analysed in conjunction, they refer to a commonphase reference. Therefore, the different phasor measurement units havelocal clocks that are synchronised with each other to within a givenprecision. Such a synchronisation of the phasor measurement units can beachieved with a known time distribution system, for example the globalpositioning (GPS) system. In a typical implementation, the phasor datais determined, for example, at least every 200, or every 100, orpreferably every 20 milliseconds, with a temporal resolution, forexample, less than 1 millisecond. In an exemplary embodiment, thetemporal resolution is less than 10 microseconds, which corresponds to aphase error of 0.2 degrees. Each measurement is associated with a timestamp derived from the synchronised local clock. The phasor datatherefore comprises time stamp data.

According to an exemplary variant, the temperature of the line isdetermined in the following way: The electric line parameters, or atleast the ohmic resistance R_(l) of the line, i.e. the real part R_(l)of the line impedance Z=R_(l)+jX_(l) are determined from measured orcomputed phasor information representing some or all of the voltage andcurrent phasors at the two ends of line.

In a first variant, it is assumed that the shunt capacitance jX_(c)remains essentially constant (e.g., ±10 percent or lesser or greater)during power line operation and is known from other measurements, designparameters or calculations. Then the two voltage phasors v₁ and v₂ aredetermined at either end of the line and one of the current phasors i₁or i₂. Let i₁ be measured. Then the impedance Z is$Z = {\frac{v_{1} - v_{2}}{i_{1} - {v_{1} \cdot {jX}_{C}}}.}$

In a second variant, no assumption on shunt impedances is made, and thetwo voltage phasors v₁ and v₂ and the two current phasors i₁ or i₂ aremeasured or determined from measurements. Determining the actualelectrical line parameters R_(l), X_(l), X_(c) from these measurementsis common knowledge. Since resulting equations for the electrical lineparameters are non-linear, numerical methods such as Newton-Raphsonapproximation are used for determining actual parameter values. Theresulting line parameters are actual values wherein they are determinedonline and represent the actual state of the power line. The averageline temperature T₁ is computed from the ohmic resistance R_(l) bymodelling a relationship between temperature and resistance as linear,i.e.R _(l) =R ₀(1+α₀(T _(l) −T ₀)),where R₀ is a known material property specified by the power lineconductor manufacturer, i.e. a reference resistance dependent on theconstruction of the line, and where α₀ is a material constant for theline cable and wherein T₀ is, for example, a reference (e.g., ambient)temperature of the line. The linear relationship is typical for commonconductor materials such as copper or aluminium. As an example, theparameter values are such that for a line temperature change of ΔT=30°C. the resistance changes by about ΔR_(l)=12%. The equation for thechosen relationship is solved for T₁, which gives the desired averageline temperature.

It will be appreciated by those skilled in the art that the presentinvention can be embodied in other specific forms without departing fromthe spirit or essential characteristics thereof. The presently disclosedembodiments are therefore considered in all respects to be illustrativeand not restricted. The scope of the invention is indicated by theappended claims rather than the foregoing description and all changesthat come within the meaning and range and equivalence thereof areintended to be embraced therein.

List of Designations

-   10 power line-   11, 11′ Phasor Measurement Units-   12 weather station-   13 electrical quantity measurement means-   14 line temperature measurement device-   15 processor

1. A method of estimating model parameters (A, B, . . . ; C_(l), . . . )of a thermal model of a power line, comprising: measuring values of anelectrical quantity (l, P) of the power line and of meteorologicalquantities (T_(a), S, W) representing ambient conditions of the powerline; calculating values of the model parameters from said measuredvalues; measuring, repeatedly during operation of the power line,momentary values (l^(i), T_(a) ^(i), S^(i), W^(i)) of the electrical andmeteorological quantities; measuring concurrently a momentary value(T_(l) ^(i)) of a temperature (T_(l)) of the power line; andcalculating, repeatedly during operation of the power line, the values(A^(i), B^(i); . . . ; C_(l) ^(i), . . . ) of the model parameters fromsaid measured values.
 2. The method according to claim 1, whereinmeasuring a momentary value (T_(l) ^(i)) of the temperature of the powerline comprises: measuring, by means of two Phasor Measurement Units,synchronized phasor data (v₁ ^(i), i₁ ^(i); v₂ ^(i), i₂ ^(i)) at twoends of the power line; computing a value (R_(l) ^(i)) of an electricalresistance (R_(l)) of the power line from the phasor data; andcomputing, from the value (R_(l) ^(i)) of the electrical resistance ofthe power line, an average line temperature as the momentary value(T_(l) ^(i)) of the temperature of the power line.
 3. The methodaccording to claim 2, wherein computing the average line temperatureinvolves an analytical expression with parameters (R₀, α₀) suitablycalibrated by means of an independent line temperature measuring device.4. The method according to claim 1, wherein measuring momentary values(T_(a) ^(i), S^(i), W^(i)) of the meteorological quantities involvesmeasuring the values by a provider of meteorological data other than anoperator of the power line.
 5. The method according to claim 1,comprising: generating a series of measured values (T_(l) ¹, T_(l) ², .. . ; u¹, u², . . . ) of the temperature of the power line and theelectrical and meteorological quantities; and adaptively calculatingupdated values (A^(k), B^(k); . . . ; C_(l) ^(k), . . . ) of said modelparameters every time a new value (T_(l) ^(k), u^(k)) of the temperatureof the power line or the electrical and meteorological quantities ismeasured.
 6. The method according to claim 1, wherein the thermal modelis a nonlinear parametric model based on a heat balance equation.
 7. Amethod for predicting a value (T_(l) ^(f)) of the line temperature ofthe power line, using a thermal model with momentary model parametervalues (A^(i), B^(i); . . . ; C_(l) ^(i), . . . ) estimated according toclaim 1, comprising: providing forecasted values (u^(f)) of theelectrical and meteorological quantities; and calculating a power linetemperature forecast (T_(l) ^(f)) based on the momentary modelparameters and the forecasted values of the electrical andmeteorological quantities.
 8. The method according to claim 7,comprising: comparing the power line temperature forecast (T_(l) ^(f))with a power line temperature limit; and calculating a maximum allowablevalue of the electrical quantity (l, P) there from.
 9. The use accordingto claim 8, comprising: using a linear thermal model for the power line;and providing the maximum allowable value of the electrical quantity (l,P) to a balance market clearing process.
 10. The method according toclaim 2, comprising generating a series of measured values (T_(l) ¹,T_(l) ², . . . ; u¹, u², . . . ) of the temperature of the power lineand the electrical and meteorological quantities; and adaptivelycalculating updated values (A^(k), B^(k); . . . ; C_(l) ^(k), . . . ) ofsaid model parameters every time a new value (T_(l) ^(k), u^(k)) of thetemperature of the power line or the electrical and meteorologicalquantities is measured.
 11. A method for predicting a value (T_(l) ^(f))of the line temperature of the power line, using a thermal model withmomentary model parameter values (A^(i), B^(i); . . . ; C_(l) ^(i), . .. ) estimated according to claim 2, comprising: providing forecastedvalues (u^(f)) of the electrical and meteorological quantities; andcalculating a power line temperature forecast (T_(l) ^(f)) based on themomentary model parameters and the forecasted values of the electricaland meteorological quantities.
 12. A method for predicting a value(T_(l) ^(f)) of the line temperature of the power line, using a thermalmodel with momentary model parameter values (A^(i), B^(i); . . . ; C_(l)^(i), . . . ) estimated according to claim 3, comprising: providingforecasted values (u^(f)) of the electrical and meteorologicalquantities; and calculating a power line temperature forecast (T_(l)^(f)) based on the momentary model parameters and the forecasted valuesof the electrical and meteorological quantities.
 13. A method forpredicting a value (T_(l) ^(f)) of the line temperature of the powerline, using a thermal model with momentary model parameter values(A^(i), B^(i); . . . ; C_(l) ^(i), . . . ) estimated according to claim4, comprising: providing forecasted values (u^(f)) of the electrical andmeteorological quantities; and calculating a power line temperatureforecast (T_(l) ^(f)) based on the momentary model parameters and theforecasted values of the electrical and meteorological quantities.
 14. Amethod for predicting a value (T_(l) ^(f)) of the line temperature ofthe power line, using a thermal model with momentary model parametervalues (A^(i), B^(i); . . . ; C_(l) ^(i), . . . ) estimated according toclaim 5, comprising: providing forecasted values (u^(f)) of theelectrical and meteorological quantities; calculating a power linetemperature forecast (T_(l) ^(f)) based on the momentary modelparameters and the forecasted values of the electrical andmeteorological quantities.
 15. A method for predicting a value (T_(l)^(f)) of the line temperature of the power line, using a thermal modelwith momentary model parameter values (A^(i), B^(i); . . . ; C_(l) ^(i),. . . ) estimated according to claim 6, comprising: providing forecastedvalues (u^(f)) of the electrical and meteorological quantities;calculating a power line temperature forecast (T_(l) ^(f)) based on themomentary model parameters and the forecasted values of the electricaland meteorological quantities.
 16. A method for predicting a value(T_(l) ^(f)) of the line temperature of the power line, using a thermalmodel with momentary model parameter values (A^(i), B^(i); . . . ; C_(l)^(i), . . . ) estimated according to claim 10, comprising: providingforecasted values (u^(f)) of the electrical and meteorologicalquantities; and calculating a power line temperature forecast (T_(l)^(f)) based on the momentary model parameters and the forecasted valuesof the electrical and meteorological quantities.
 17. A method ofestimating a parameter of a thermal model of a power line, comprising:measuring a value of an electrical quantity of the power line and atleast one meteorological quantity representing an ambient condition ofthe power line; calculating a value of the parameter of the thermalmodel from said electrical quantity and said meteorological quantity;measuring, during operation of the power line, a momentary value of eachthe electrical quantity an the meteorological quantity; measuring amomentary value of a temperature of the power line; and calculating,during operation of the power line, a value of the parameter from saidmeasured values of the electrical quantity, the meteorological quantityand the temperature.